Question

A simple model for a person running the 100m dash is to assume the sprinter runs with constant acceleration until reaching top speed, then maintains that speed through the finish line. If a sprinter reaches his top speed of 11.2 m/s in 12.4 s, what will be his total time?

Answer 1

Let the distance traveled from the start until top speed is reached be d1.
Let the distance traveled between reaching top speed and the finish be d2.
The average speed from the start to reaching top speed = 11.2/2 = 5.6 m/s.
\[\large d _{1}=5.6\times12.4\ .....(1)\]
\[\large d _{2}=100-d _{1}\ ........(2)\]
Let the time taken to travel the distance d2 be t2.
\[\large t _{2}=\frac{d _{2}}{11.2}\ .....(3)\]
The total time to run the 100 m is given by:
\[\large Total\ time=11.2+t _{2}=you\ can\ calculate\]

Answer 2

Sorry for mistake in last line. Correction follows:
\[\large Total \ time=12.4+t _{2}=you\ can\ calculate\]

Answer 3

@edwardp Can you follow the explanation?

Answer 4

oh thank you, i got it :)

Answer 5

You're welcome :)